%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO558+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:18:06 AM UTC 2026
% Result : Theorem 15.41s 4.91s
% Output : CNFRefutation 15.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 30
% Syntax : Number of formulae : 180 ( 73 unt; 0 def)
% Number of atoms : 382 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 326 ( 124 ~; 120 |; 51 &)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-5 aty)
% Number of variables : 501 ( 79 sgn 177 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ruleD1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('theBenchmark.p',ruleD1) ).
fof(ruleD2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('theBenchmark.p',ruleD2) ).
fof(ruleD3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('theBenchmark.p',ruleD3) ).
fof(ruleD4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('theBenchmark.p',ruleD4) ).
fof(ruleD5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('theBenchmark.p',ruleD5) ).
fof(ruleD8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('theBenchmark.p',ruleD8) ).
fof(ruleD9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('theBenchmark.p',ruleD9) ).
fof(ruleD12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,C)
& cong(O,A,O,B) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleD12) ).
fof(ruleD14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('theBenchmark.p',ruleD14) ).
fof(ruleD15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('theBenchmark.p',ruleD15) ).
fof(ruleD16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('theBenchmark.p',ruleD16) ).
fof(ruleD17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('theBenchmark.p',ruleD17) ).
fof(ruleD19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('theBenchmark.p',ruleD19) ).
fof(ruleD23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('theBenchmark.p',ruleD23) ).
fof(ruleD24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('theBenchmark.p',ruleD24) ).
fof(ruleD39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('theBenchmark.p',ruleD39) ).
fof(ruleD40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('theBenchmark.p',ruleD40) ).
fof(ruleD42b,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('theBenchmark.p',ruleD42b) ).
fof(ruleD43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('theBenchmark.p',ruleD43) ).
fof(ruleD45,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
file('theBenchmark.p',ruleD45) ).
fof(ruleD51,axiom,
! [A,B,C,O,M] :
( ( eqangle(A,B,A,C,O,B,O,M)
& coll(M,B,C)
& circle(O,A,B,C) )
=> midp(M,B,C) ),
file('theBenchmark.p',ruleD51) ).
fof(ruleD53,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('theBenchmark.p',ruleD53) ).
fof(ruleD56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('theBenchmark.p',ruleD56) ).
fof(ruleD64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('theBenchmark.p',ruleD64) ).
fof(ruleD65,axiom,
! [A,B,C,D,O] :
( ( coll(O,B,D)
& coll(O,A,C)
& para(A,B,C,D) )
=> eqratio(O,A,A,C,O,B,B,D) ),
file('theBenchmark.p',ruleD65) ).
fof(ruleD66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('theBenchmark.p',ruleD66) ).
fof(ruleD75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( cong(P,Q,U,V)
& eqratio(A,B,C,D,P,Q,U,V) )
=> cong(A,B,C,D) ),
file('theBenchmark.p',ruleD75) ).
fof(ruleX11,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('theBenchmark.p',ruleX11) ).
fof(ruleX13,axiom,
! [A,B,C,D,M] :
? [O] :
( ( midp(M,A,B)
& para(A,B,C,D)
& cyclic(A,B,C,D) )
=> circle(O,A,B,C) ),
file('theBenchmark.p',ruleX13) ).
fof(exemplo6GDDFULL012018,conjecture,
! [A,C,K,O,N,B,G,O1,M,NWPNT1,NWPNT2,NWPNT3] :
( ( circle(O1,K,M,NWPNT3)
& circle(G,A,M,NWPNT2)
& circle(O1,K,N,B)
& circle(G,A,C,B)
& coll(B,C,N)
& coll(B,A,K)
& circle(O,A,N,NWPNT1)
& circle(O,A,C,K) )
=> perp(B,M,M,O) ),
file('theBenchmark.p',exemplo6GDDFULL012018) ).
fof(exemplo6GDDFULL012018_neg,negated_conjecture,
~ ! [A,C,K,O,N,B,G,O1,M,NWPNT1,NWPNT2,NWPNT3] :
( ( circle(O1,K,M,NWPNT3)
& circle(G,A,M,NWPNT2)
& circle(O1,K,N,B)
& circle(G,A,C,B)
& coll(B,C,N)
& coll(B,A,K)
& circle(O,A,N,NWPNT1)
& circle(O,A,C,K) )
=> perp(B,M,M,O) ),
inference(assume_negation,[status(cth)],[exemplo6GDDFULL012018]) ).
cnf(c_97,plain,
( circle(A,B,C,D)
| ~ cong(A,B,A,D)
| ~ cong(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD12]) ).
cnf(c_100,plain,
( midp(E,C,D)
| ~ eqangle(B,C,B,D,A,C,A,E)
| ~ coll(E,C,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD51]) ).
cnf(c_101,plain,
( perp(B,C,C,D)
| ~ coll(A,B,D)
| ~ circle(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD53]) ).
fof(nnf_87,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(fof_nnf,[status(thm)],[ruleX11]) ).
fof(sk_ruleX11,plain,
! [A,B,C,O] :
( perp(sK0(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0(A,B,C,O))],[nnf_87]) ).
cnf(c_102,plain,
( perp(sK0(B,C,D,A),B,B,A)
| ~ circle(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_ruleX11]) ).
fof(nnf_89,plain,
! [A,B,C,D,M] :
? [O] :
( circle(O,A,B,C)
| ~ midp(M,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(fof_nnf,[status(thm)],[ruleX13]) ).
fof(sk_ruleX13,plain,
! [A,B,C,D,M] :
( circle(sK1(A,B,C,D,M),A,B,C)
| ~ midp(M,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(O,sK1(A,B,C,D,M))],[nnf_89]) ).
cnf(c_107,plain,
( circle(sK1(A,B,C,D,E),A,B,C)
| ~ midp(E,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_ruleX13]) ).
fof(nnf_95,plain,
? [A,C,K,O,N,B,G,O1,M,NWPNT1,NWPNT2,NWPNT3] :
( ~ perp(B,M,M,O)
& circle(O1,K,M,NWPNT3)
& circle(G,A,M,NWPNT2)
& circle(O1,K,N,B)
& circle(G,A,C,B)
& coll(B,C,N)
& coll(B,A,K)
& circle(O,A,N,NWPNT1)
& circle(O,A,C,K) ),
inference(fof_nnf,[status(thm)],[exemplo6GDDFULL012018_neg]) ).
fof(sk_exemplo6GDDFULL012018_neg,plain,
( ~ perp(sK8,sK9,sK9,sK2)
& circle(sK6,sK5,sK9,sK13)
& circle(sK11,sK3,sK9,sK12)
& circle(sK6,sK5,sK7,sK8)
& circle(sK11,sK3,sK4,sK8)
& coll(sK8,sK4,sK7)
& coll(sK8,sK3,sK5)
& circle(sK2,sK3,sK7,sK10)
& circle(sK2,sK3,sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK7,sK10,sK8,sK11,sK6,sK9,sK12,sK13]),skolemize(A,sK3),skolemize(C,sK4),skolemize(K,sK5),skolemize(O,sK2),skolemize(N,sK7),skolemize(B,sK8),skolemize(G,sK11),skolemize(O1,sK6),skolemize(M,sK9),skolemize(NWPNT1,sK10),skolemize(NWPNT2,sK12),skolemize(NWPNT3,sK13)],[nnf_95]) ).
cnf(c_109,negated_conjecture,
circle(sK2,sK3,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012018_neg]) ).
cnf(c_112,negated_conjecture,
circle(sK6,sK5,sK7,sK8),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012018_neg]) ).
cnf(c_148,negated_conjecture,
perp(sK0(sK5,sK7,sK8,sK6),sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_112,c_102]) ).
cnf(c_190,negated_conjecture,
perp(sK0(sK3,sK4,sK5,sK2),sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_109,c_102]) ).
cnf(c_217,plain,
( perp(A,B,B,C)
| ~ coll(sK1(A,B,C,D,E),A,C)
| ~ midp(E,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(resolve,[status(thm)],[c_107,c_101]) ).
cnf(c_233,plain,
( ~ cong(E,D,E,C)
| ~ cong(E,D,E,B)
| midp(A,B,C)
| ~ eqangle(D,B,D,C,E,B,E,A)
| ~ coll(A,B,C) ),
inference(resolve,[status(thm)],[c_100,c_97]) ).
cnf(c_237,negated_conjecture,
~ perp(sK8,sK9,sK9,sK2),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012018_neg]) ).
cnf(c_239,negated_conjecture,
coll(sK8,sK3,sK5),
inference(split_conjunct,[status(thm)],[sk_exemplo6GDDFULL012018_neg]) ).
cnf(c_270,plain,
( cong(A,B,C,D)
| ~ cong(E,F,V6,V7)
| ~ eqratio(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD75]) ).
cnf(c_278,plain,
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(clausify,[status(thm)],[ruleD66]) ).
cnf(c_279,plain,
( eqratio(E,A,A,C,E,B,B,D)
| ~ coll(E,B,D)
| ~ coll(E,A,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD65]) ).
cnf(c_280,plain,
( midp(A,D,E)
| ~ para(B,E,C,D)
| ~ para(B,D,C,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD64]) ).
cnf(c_288,plain,
( perp(A,C,B,D)
| ~ cong(A,D,C,D)
| ~ cong(A,B,C,B) ),
inference(clausify,[status(thm)],[ruleD56]) ).
cnf(c_294,plain,
( midp(D,B,E)
| ~ coll(D,B,E)
| ~ para(A,D,C,E)
| ~ midp(A,B,C) ),
inference(clausify,[status(thm)],[ruleD45]) ).
cnf(c_296,plain,
( cong(A,B,D,E)
| ~ eqangle(C,A,C,B,F,D,F,E)
| ~ cyclic(A,B,C,F)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD43]) ).
cnf(c_297,plain,
( cyclic(B,C,A,D)
| ~ coll(A,D,C)
| ~ eqangle(A,B,A,C,D,B,D,C) ),
inference(clausify,[status(thm)],[ruleD42b]) ).
cnf(c_300,plain,
( eqangle(A,B,E,F,C,D,E,F)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD40]) ).
cnf(c_301,plain,
( para(A,B,E,F)
| ~ eqangle(A,B,C,D,E,F,C,D) ),
inference(clausify,[status(thm)],[ruleD39]) ).
cnf(c_316,plain,
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD24]) ).
cnf(c_317,plain,
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD23]) ).
cnf(c_321,plain,
( eqangle(C,D,A,B,V6,V7,E,F)
| ~ eqangle(A,B,C,D,E,F,V6,V7) ),
inference(clausify,[status(thm)],[ruleD19]) ).
cnf(c_323,plain,
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD17]) ).
cnf(c_324,plain,
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD16]) ).
cnf(c_325,plain,
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD15]) ).
cnf(c_326,plain,
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD14]) ).
cnf(c_330,plain,
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD9]) ).
cnf(c_331,plain,
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD8]) ).
cnf(c_334,plain,
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD5]) ).
cnf(c_335,plain,
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(clausify,[status(thm)],[ruleD4]) ).
cnf(c_336,plain,
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD3]) ).
cnf(c_337,plain,
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD2]) ).
cnf(c_338,plain,
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(clausify,[status(thm)],[ruleD1]) ).
cnf(c_354,plain,
( ~ cong(D,C,D,B)
| midp(A,B,B)
| ~ eqangle(C,B,C,B,D,B,D,A)
| ~ coll(A,B,B) ),
inference(factor,[status(thm)],[c_233]) ).
cnf(c_387,plain,
( cyclic(B,C,D,D)
| ~ cyclic(A,B,C,D) ),
inference(factor,[status(thm)],[c_323]) ).
cnf(c_392,plain,
( coll(C,C,A)
| ~ coll(A,B,C) ),
inference(factor,[status(thm)],[c_336]) ).
cnf(c_534,plain,
( para(A,B,sK3,sK2)
| ~ perp(A,B,sK0(sK3,sK4,sK5,sK2),sK3) ),
inference(resolve,[status(thm)],[c_330,c_190]) ).
cnf(c_537,plain,
( para(A,B,sK5,sK6)
| ~ perp(A,B,sK0(sK5,sK7,sK8,sK6),sK5) ),
inference(resolve,[status(thm)],[c_330,c_148]) ).
cnf(c_540,plain,
perp(sK3,sK2,sK0(sK3,sK4,sK5,sK2),sK3),
inference(resolve,[status(thm)],[c_331,c_190]) ).
cnf(c_543,plain,
perp(sK5,sK6,sK0(sK5,sK7,sK8,sK6),sK5),
inference(resolve,[status(thm)],[c_331,c_148]) ).
cnf(c_558,plain,
coll(sK8,sK5,sK3),
inference(resolve,[status(thm)],[c_338,c_239]) ).
cnf(c_570,plain,
coll(sK3,sK3,sK8),
inference(resolve,[status(thm)],[c_558,c_392]) ).
cnf(c_602,plain,
coll(sK3,sK8,sK3),
inference(resolve,[status(thm)],[c_570,c_338]) ).
cnf(c_648,plain,
coll(sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_602,c_392]) ).
cnf(c_685,plain,
( coll(A,sK3,sK3)
| ~ coll(sK3,sK3,A) ),
inference(resolve,[status(thm)],[c_648,c_336]) ).
cnf(c_920,plain,
para(sK3,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_540,c_534]) ).
cnf(c_973,plain,
para(sK3,sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_920,c_335]) ).
cnf(c_974,plain,
eqangle(sK3,sK2,A,B,sK3,sK2,A,B),
inference(resolve,[status(thm)],[c_920,c_300]) ).
cnf(c_976,plain,
( eqratio(A,sK3,sK3,sK3,A,sK2,sK2,sK2)
| ~ coll(A,sK2,sK2)
| ~ coll(A,sK3,sK3) ),
inference(resolve,[status(thm)],[c_920,c_279]) ).
cnf(c_977,plain,
coll(sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_920,c_278]) ).
cnf(c_984,plain,
coll(sK2,sK2,sK3),
inference(resolve,[status(thm)],[c_977,c_392]) ).
cnf(c_985,plain,
coll(sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_977,c_337]) ).
cnf(c_994,plain,
coll(sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_984,c_392]) ).
cnf(c_1001,plain,
coll(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_985,c_392]) ).
cnf(c_1004,plain,
coll(sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_994,c_685]) ).
cnf(c_1017,plain,
para(sK5,sK6,sK5,sK6),
inference(resolve,[status(thm)],[c_543,c_537]) ).
cnf(c_1971,plain,
para(sK2,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_973,c_334]) ).
cnf(c_1986,plain,
para(sK5,sK6,sK6,sK5),
inference(resolve,[status(thm)],[c_1017,c_335]) ).
cnf(c_1987,plain,
eqangle(sK5,sK6,A,B,sK5,sK6,A,B),
inference(resolve,[status(thm)],[c_1017,c_300]) ).
cnf(c_2611,plain,
para(sK2,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_1971,c_335]) ).
cnf(c_2627,plain,
para(sK6,sK5,sK5,sK6),
inference(resolve,[status(thm)],[c_1986,c_334]) ).
cnf(c_2739,plain,
eqangle(sK2,sK3,A,B,sK2,sK3,A,B),
inference(resolve,[status(thm)],[c_2611,c_300]) ).
cnf(c_2752,plain,
para(sK6,sK5,sK6,sK5),
inference(resolve,[status(thm)],[c_2627,c_335]) ).
cnf(c_2843,plain,
eqangle(sK6,sK5,A,B,sK6,sK5,A,B),
inference(resolve,[status(thm)],[c_2752,c_300]) ).
cnf(c_13358,plain,
( ~ cong(sK3,sK3,sK3,sK2)
| midp(sK2,sK2,sK2)
| ~ coll(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_974,c_354]) ).
cnf(c_2977,plain,
( ~ cong(sK3,sK3,sK3,sK2)
| midp(sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_1001,c_13358]) ).
cnf(c_2978,plain,
eqangle(A,B,sK3,sK2,A,B,sK3,sK2),
inference(resolve,[status(thm)],[c_974,c_321]) ).
cnf(c_13359,plain,
( eqratio(sK2,sK3,sK3,sK3,sK2,sK2,sK2,sK2)
| ~ coll(sK2,sK3,sK3) ),
inference(resolve,[status(thm)],[c_976,c_1001]) ).
cnf(c_2993,plain,
eqratio(sK2,sK3,sK3,sK3,sK2,sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_1004,c_13359]) ).
cnf(c_7390,plain,
( cyclic(sK6,A,sK5,sK5)
| ~ coll(sK5,sK5,A) ),
inference(resolve,[status(thm)],[c_1987,c_297]) ).
cnf(c_7391,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK5,sK5)
| ~ cyclic(sK6,A,sK5,A)
| ~ cyclic(sK6,A,sK5,sK6) ),
inference(resolve,[status(thm)],[c_1987,c_296]) ).
cnf(c_7480,plain,
( cyclic(sK3,A,sK2,sK2)
| ~ coll(sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_2739,c_297]) ).
cnf(c_7526,plain,
( cyclic(sK5,A,sK6,sK6)
| ~ coll(sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_2843,c_297]) ).
cnf(c_7588,plain,
para(A,B,A,B),
inference(resolve,[status(thm)],[c_2978,c_301]) ).
cnf(c_13360,plain,
( cyclic(A,sK2,sK3,sK3)
| ~ coll(sK3,sK3,sK2) ),
inference(resolve,[status(thm)],[c_2978,c_297]) ).
cnf(c_7590,plain,
cyclic(A,sK2,sK3,sK3),
inference(resolve,[status(thm)],[c_994,c_13360]) ).
cnf(c_13361,plain,
( cong(A,sK2,A,sK2)
| ~ cyclic(A,sK2,sK3,sK3)
| ~ cyclic(A,sK2,sK3,sK2)
| ~ cyclic(A,sK2,sK3,A) ),
inference(resolve,[status(thm)],[c_2978,c_296]) ).
cnf(c_7591,plain,
( cong(A,sK2,A,sK2)
| ~ cyclic(A,sK2,sK3,sK2)
| ~ cyclic(A,sK2,sK3,A) ),
inference(resolve,[status(thm)],[c_7590,c_13361]) ).
cnf(c_7613,plain,
coll(A,B,B),
inference(resolve,[status(thm)],[c_7588,c_278]) ).
cnf(c_7745,plain,
coll(A,A,B),
inference(resolve,[status(thm)],[c_7613,c_392]) ).
cnf(c_7753,plain,
cyclic(sK5,A,sK6,sK6),
inference(resolve,[status(thm)],[c_7745,c_7526]) ).
cnf(c_7755,plain,
cyclic(sK3,A,sK2,sK2),
inference(resolve,[status(thm)],[c_7745,c_7480]) ).
cnf(c_7756,plain,
cyclic(sK6,A,sK5,sK5),
inference(resolve,[status(thm)],[c_7745,c_7390]) ).
cnf(c_7925,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK5,A)
| ~ cyclic(sK6,A,sK5,sK6) ),
inference(resolve,[status(thm)],[c_7756,c_7391]) ).
cnf(c_13362,plain,
( coll(B,C,A)
| ~ coll(A,A,B) ),
inference(resolve,[status(thm)],[c_7745,c_336]) ).
cnf(c_8010,plain,
coll(A,B,C),
inference(resolve,[status(thm)],[c_7745,c_13362]) ).
cnf(c_8033,plain,
( midp(D,B,E)
| ~ para(A,D,C,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_8010,c_294]) ).
cnf(c_8040,plain,
( perp(A,B,B,C)
| ~ midp(E,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(resolve,[status(thm)],[c_8010,c_217]) ).
cnf(c_8287,plain,
cyclic(A,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_7590,c_325]) ).
cnf(c_8330,plain,
cyclic(sK5,sK6,A,sK6),
inference(resolve,[status(thm)],[c_7753,c_325]) ).
cnf(c_8364,plain,
cyclic(sK3,sK2,A,sK2),
inference(resolve,[status(thm)],[c_7755,c_325]) ).
cnf(c_8365,plain,
cyclic(A,sK3,sK2,sK2),
inference(resolve,[status(thm)],[c_7755,c_324]) ).
cnf(c_8492,plain,
cyclic(sK3,A,sK2,sK3),
inference(resolve,[status(thm)],[c_8287,c_324]) ).
cnf(c_8572,plain,
cyclic(sK5,sK6,sK6,A),
inference(resolve,[status(thm)],[c_8330,c_326]) ).
cnf(c_8573,plain,
cyclic(sK6,sK5,A,sK6),
inference(resolve,[status(thm)],[c_8330,c_324]) ).
cnf(c_8666,plain,
cyclic(sK3,sK2,sK2,A),
inference(resolve,[status(thm)],[c_8364,c_326]) ).
cnf(c_8667,plain,
cyclic(sK2,sK3,A,sK2),
inference(resolve,[status(thm)],[c_8364,c_324]) ).
cnf(c_8683,plain,
cyclic(A,sK2,sK3,sK2),
inference(resolve,[status(thm)],[c_8365,c_325]) ).
cnf(c_8696,plain,
( cong(A,sK2,A,sK2)
| ~ cyclic(A,sK2,sK3,A) ),
inference(resolve,[status(thm)],[c_8683,c_7591]) ).
cnf(c_8951,plain,
( cyclic(A,sK2,sK3,B)
| ~ cyclic(sK3,A,sK2,B) ),
inference(resolve,[status(thm)],[c_8492,c_323]) ).
cnf(c_9051,plain,
cyclic(sK6,sK6,A,A),
inference(resolve,[status(thm)],[c_8572,c_387]) ).
cnf(c_13363,plain,
( cyclic(sK6,sK6,A,B)
| ~ cyclic(sK5,sK6,sK6,A) ),
inference(resolve,[status(thm)],[c_8572,c_323]) ).
cnf(c_9053,plain,
cyclic(sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_8572,c_13363]) ).
cnf(c_9067,plain,
cyclic(sK6,A,sK5,sK6),
inference(resolve,[status(thm)],[c_8573,c_325]) ).
cnf(c_9083,plain,
( cong(sK6,A,sK6,A)
| ~ cyclic(sK6,A,sK5,A) ),
inference(resolve,[status(thm)],[c_9067,c_7925]) ).
cnf(c_13364,plain,
( cyclic(sK2,sK2,A,B)
| ~ cyclic(sK3,sK2,sK2,A) ),
inference(resolve,[status(thm)],[c_8666,c_323]) ).
cnf(c_9524,plain,
cyclic(sK2,sK2,A,B),
inference(resolve,[status(thm)],[c_8666,c_13364]) ).
cnf(c_9540,plain,
( cyclic(sK3,A,sK2,B)
| ~ cyclic(sK2,sK3,A,B) ),
inference(resolve,[status(thm)],[c_8667,c_323]) ).
cnf(c_13365,plain,
( cyclic(sK6,A,B,A)
| ~ cyclic(sK6,sK6,A,B) ),
inference(resolve,[status(thm)],[c_9051,c_323]) ).
cnf(c_9944,plain,
cyclic(sK6,A,B,A),
inference(resolve,[status(thm)],[c_9053,c_13365]) ).
cnf(c_9957,plain,
cong(sK6,A,sK6,A),
inference(resolve,[status(thm)],[c_9944,c_9083]) ).
cnf(c_13366,plain,
( cyclic(sK6,A,B,C)
| ~ cyclic(sK6,sK6,A,B) ),
inference(resolve,[status(thm)],[c_9053,c_323]) ).
cnf(c_9999,plain,
cyclic(sK6,A,B,C),
inference(resolve,[status(thm)],[c_9053,c_13366]) ).
cnf(c_13367,plain,
( cyclic(sK2,A,B,C)
| ~ cyclic(sK2,sK2,A,B) ),
inference(resolve,[status(thm)],[c_9524,c_323]) ).
cnf(c_10436,plain,
cyclic(sK2,A,B,C),
inference(resolve,[status(thm)],[c_9524,c_13367]) ).
cnf(c_10448,plain,
cyclic(sK3,A,sK2,B),
inference(resolve,[status(thm)],[c_10436,c_9540]) ).
cnf(c_10479,plain,
cyclic(A,sK2,sK3,B),
inference(resolve,[status(thm)],[c_10448,c_8951]) ).
cnf(c_10482,plain,
cong(A,sK2,A,sK2),
inference(resolve,[status(thm)],[c_10479,c_8696]) ).
cnf(c_13368,plain,
( perp(sK6,sK6,A,B)
| ~ cong(sK6,A,sK6,A) ),
inference(resolve,[status(thm)],[c_9957,c_288]) ).
cnf(c_11062,plain,
perp(sK6,sK6,A,B),
inference(resolve,[status(thm)],[c_9957,c_13368]) ).
cnf(c_13369,plain,
( cyclic(A,B,C,D)
| ~ cyclic(sK6,A,B,C) ),
inference(resolve,[status(thm)],[c_9999,c_323]) ).
cnf(c_11287,plain,
cyclic(A,B,C,D),
inference(resolve,[status(thm)],[c_9999,c_13369]) ).
cnf(c_11301,plain,
( perp(A,B,B,C)
| ~ midp(E,A,B)
| ~ para(A,B,C,D) ),
inference(resolve,[status(thm)],[c_11287,c_8040]) ).
cnf(c_12411,plain,
perp(A,B,sK6,sK6),
inference(resolve,[status(thm)],[c_11062,c_331]) ).
cnf(c_13370,plain,
( para(A,B,C,D)
| ~ perp(A,B,sK6,sK6) ),
inference(resolve,[status(thm)],[c_11062,c_330]) ).
cnf(c_12412,plain,
para(A,B,C,D),
inference(resolve,[status(thm)],[c_12411,c_13370]) ).
cnf(c_12422,plain,
( perp(B,C,C,D)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_12412,c_11301]) ).
cnf(c_12431,plain,
( midp(D,B,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_12412,c_8033]) ).
cnf(c_13371,plain,
( midp(A,E,D)
| ~ para(B,D,C,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_12412,c_280]) ).
cnf(c_12435,plain,
( midp(A,D,E)
| ~ midp(A,B,C) ),
inference(resolve,[status(thm)],[c_12412,c_13371]) ).
cnf(c_13372,plain,
( cong(sK2,sK3,sK3,sK3)
| ~ cong(sK2,sK2,sK2,sK2) ),
inference(resolve,[status(thm)],[c_2993,c_270]) ).
cnf(c_13060,plain,
cong(sK2,sK3,sK3,sK3),
inference(resolve,[status(thm)],[c_10482,c_13372]) ).
cnf(c_13061,plain,
cong(sK3,sK3,sK2,sK3),
inference(resolve,[status(thm)],[c_13060,c_316]) ).
cnf(c_13064,plain,
cong(sK3,sK3,sK3,sK2),
inference(resolve,[status(thm)],[c_13061,c_317]) ).
cnf(c_13070,plain,
midp(sK2,sK2,sK2),
inference(resolve,[status(thm)],[c_13064,c_2977]) ).
cnf(c_13071,plain,
midp(sK2,A,B),
inference(resolve,[status(thm)],[c_13070,c_12435]) ).
cnf(c_13268,plain,
midp(A,B,C),
inference(resolve,[status(thm)],[c_13071,c_12431]) ).
cnf(c_13356,plain,
perp(A,B,B,C),
inference(resolve,[status(thm)],[c_13268,c_12422]) ).
cnf(c_13357,plain,
$false,
inference(resolve,[status(thm)],[c_13356,c_237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO558+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.40 % Computer : n008.cluster.edu
% 0.08/0.40 % Model : x86_64 x86_64
% 0.08/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.40 % Memory : 8046.5625MB
% 0.08/0.40 % OS : Linux 6.8.0-71-generic
% 0.08/0.40 % CPULimit : 300
% 0.08/0.40 % WCLimit : 300
% 0.08/0.40 % DateTime : Fri Sep 25 13:42:24 UTC 2026
% 0.08/0.40 % CPUTime :
% 0.08/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.40 % Process 1180107 was started by sandbox on n008,
% 0.08/0.40 % Fri Sep 25 13:42:24 2026
% 0.08/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.44
% 0.08/0.44 % From the command line: assign(max_seconds, 300).
% 15.41/4.91
% 15.41/4.91 % given #500 (A,wt=40): 484 -perp(c1,c1,f12(c1,c9,c11,c7),c7) | coll(f10(c1,f12(c1,c9,c11,c7),c7,c1),c7,f12(c1,c9,c11,c7)). [resolve(250,b,134,a)].
% 15.41/4.91
% 15.41/4.91 % given #1000 (T,wt=9): 2093 coll(c3,c5,c8). [resolve(2034,a,337,a)].
% 15.41/4.91
% 15.41/4.91 % given #1500 (A,wt=28): 1146 coll(f17(f12(c1,c5,c10,c4),c4,c1,c1,c3),c1,c3). [resolve(1079,a,433,a)].
% 15.41/4.91
% 15.41/4.91 % given #2000 (W,wt=13): 2327 -coll(c8,c1,A) | coll(A,c1,c8). [resolve(2145,a,336,b)].
% 15.41/4.91
% 15.41/4.91 % given #2500 (T,wt=14): 2781 -midp(c6,c3,c5) | cong(c5,c3,c5,c5). [resolve(2641,a,289,b)].
% 15.41/4.91
% 15.41/4.91 % given #3000 (W,wt=10): 10255 perp(c1,c1,c1,A). [back_unit_del(8544),unit_del(a,10247)].
% 15.41/4.91
% 15.41/4.91 % SZS status Theorem for theBenchmark
% 15.41/4.91
% 15.41/4.91 % Proof 1 at 1.81 (+ 0.44) seconds.
% 15.41/4.91 % Length of proof is 158.
% 15.41/4.91 % Level of proof is 25.
% 15.41/4.91 % Maximum clause weight is 38.000.
% 15.41/4.91 % Given clauses 3292.
% 15.41/4.91
% 15.41/4.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------